相关论文: Shape optimization for superconductors governed by…

This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…

We propose and investigate a mesh deformation technique for PDE constrained shape optimization. Introducing a gradient penalization to the inner product for linearized shape spaces, mesh degeneration can be prevented within the optimization…

The curse of dimensionality presents a pervasive challenge in optimization problems, with exponential expansion of the search space rapidly causing traditional algorithms to become inefficient or infeasible. An adaptive sampling strategy is…

In this paper, we present solvable, convex formulations of $H_2$-optimal state estimation and state-feedback control problems for a general class of linear Partial Differential Equations (PDEs) with one spatial dimension. These convex…

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional…

As widely used electrochemical storage devices, supercapacitors deliver higher power density than batteries, but suffer from significantly lower energy density. In this work, we propose a topology optimization model for electrode structure…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

We develop a novel frequency-based H-infinity control method for a large class of infinite-dimensional Linear-Time-Invariant systems in transfer function form. Major benefits of our approach is that reduction or identification techniques…

Topology optimization is used to systematically design contact-aided thermo-mechanical regulators, i.e. components whose effective thermal conductivity is tunable by mechanical deformation and contact. The thermo-mechanical interactions are…

We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…

We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…

The U-curve optimization problem is characterized by a decomposable in U-shaped curves cost function over the chains of a Boolean lattice. This problem can be applied to model the classical feature selection problem in Machine Learning.…

This article discusses an optimal control problem for a phase field model of two immiscible incompressible fluid flow, incorporating surface tension effects. The optimal control problem is defined with a $L^2$-cost functional and subject to…

Shape optimization involves the minimization of a cost function defined over a set of shapes, often governed by a partial differential equation (PDE). In the absence of closed-form solutions, one relies on numerical methods to approximate…

In this article, we develop and analyze a finite element method with the first family N\'ed\'elec elements of the lowest degree for solving a Maxwell interface problem modeled by a $\mathbf{H}(\text{curl})$-elliptic equation on unfitted…

In this paper we study the asymptotic behaviour of the quasilinear $curl$-$curl$ equation of 3D magnetostatics with respect to a singular perturbation of the differential operator and prove the existence of the topological derivative using…

We present an initial implementation of a probabilistic PDE-constrained shape optimization algorithm. Our method is based on a novel probabilistic representation of the shape derivative, which is evaluated using Monte Carlo sampling; and…

We consider optimal control problems of elliptic PDEs on hypersurfaces in 2- or 3-dimensional Euclidean space. The leading part of the PDE is given by the Laplace-Beltrami operator, which is discretized by finite elements on a polyhedral…

Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…

In this paper we consider a shape optimization problem in which the data in the cost functional and in the state equation may change sign, and so no monotonicity assumption is satisfied. Nevertheless, we are able to prove that an optimal…